Engineering physics — the applied-physics sub-discipline that bridges fundamental physics and engineering design, covering device physics, instrumentation, measurement science, and control systems. Foundations: (1) Semiconductor device…
engineering-physics
Shockley diode: I = I_s·(exp(q·V/k_B·T) - 1)
The Shockley ideal diode equation — the foundational I-V relation for a p-n junction: I = I_s·(exp(q·V/k_B·T) - 1), where I_s is the…
MOSFET saturation: I_D = (K/2)·(V_GS - V_T)²
The MOSFET saturation-region drain current follows the 'square-law' model: I_D = (K/2)·(V_GS - V_T)², where K = μ_n·C_ox·W/L (μ_n electron…
RC low-pass: f_3dB = 1/(2π·R·C); |H|² at ω_c = 1/2
The first-order RC low-pass filter has transfer function H(ω) = 1/(1 + j·ω·R·C), hence magnitude-squared |H(ω)|² = 1/(1 + (ω·R·C)²). The…
Shockley zero-bias: I(V=0) = 0
Sympy-exact witness of the Shockley-diode zero-bias identity. Setup: I = I_s·(exp(q·V/(T·k_B)) - 1) as a four-symbol function. Identity:…
MOSFET anchor: I_D(V_GS=V_T)=0; I_D(V_GS=2·V_T)=K·V_T²/2
Sympy-exact witness of the MOSFET-saturation anchor identities. Setup: I_D = (K/2)·(V_GS - V_T)² as a three-symbol polynomial. Identity 1…
RC low-pass cutoff: |H|²(ω=0)=1; |H|²(ω=1/RC)=1/2
Sympy-exact witness of the RC low-pass limiting magnitudes. Setup: |H(ω)|² = 1/(1 + (ω·R·C)²) as a three-symbol rational function. …
Bernoulli equation along streamline p + (1/2)rho v^2 + rho g h = const; Rolle invariant
Bernoulli-streamline framework for inviscid incompressible flow (Bernoulli 1738 Hydrodynamica). Setup: along a streamline in steady…
Euler-Bernoulli beam EI w''''(x) = q(x); 4th-order ODE; Bernstein basis FEM
Euler-Bernoulli beam-bending framework (Bernoulli D 1742; Euler 1750 Methodus inveniendi lineas curvas). Setup: small-deflection bending of…
PID controller transfer function G(s) = K_p + K_i/s + K_d s; Pade rational form
PID (Proportional-Integral-Derivative) controller framework (Minorsky 1922; Ziegler-Nichols 1942 Trans ASME 64, 759). Setup: closed-loop…
Theorem: dB/ds = 0 for steady inviscid incompressible Bernoulli invariant (Rolle)
Theorem (Bernoulli-Rolle canonical): along a steady inviscid incompressible streamline, B(s) = p + (1/2) rho v^2 + rho g h is constant in…
Theorem: w(L) - q L^4/(8 EI) = 0 (cantilever end-deflection identity)
Theorem (cantilever-end-deflection canonical): for the uniformly-loaded cantilever solution w(x) = q x^2 (6 L^2 - 4 L x + x^2)/(24 EI),…
Theorem: G(s) s - (K_d s^2 + K_p s + K_i) = 0 (PID rational clearance identity)
Theorem (PID-rational-clearance canonical): G(s) = K_p + K_i/s + K_d s multiplied by s gives K_p s + K_i + K_d s^2 = K_d s^2 + K_p s + K_i,…
PID control (Ziegler-Nichols 1942)
Ziegler-Nichols 1942 tuning rules: u(t) = K_p e + K_i integral e + K_d de/dt; ultimate-gain method gives K_p = 0.6 K_u, T_i = T_u/2, T_d =…
Kalman filter (1960)
R E Kalman 1960 LQG state-estimator: optimal recursive Bayes for linear-Gaussian dynamics + observations; prediction-update cycle;…
Nyquist stability criterion (1932)
H Nyquist 1932 frequency-domain stability: Nyquist plot encirclements of -1 = number of unstable poles in closed-loop; Bode 1945 extends…
Finite element method (Courant 1943)
Courant 1943 + Argyris 1955 + Clough 1956 FEM: discretize PDE on simplicial mesh; weak form Galerkin minimization; basis of…
Lyapunov second method (1892)
Lyapunov 1892 doctoral thesis: V(x) > 0, dV/dt < 0 in neighborhood -> origin asymptotically stable; converse Massera 1949; basis of…
Model predictive control (MPC)
Richalet 1976 IDCOM + Cutler-Ramaker 1980 DMC: receding-horizon optimization solves QP at each timestep; constraint-handling +…
Buckingham π (1914)
E Buckingham 1914 + Vaschy 1892 π-theorem; modern modern foundational text + Reynolds + Mach + 2024 ML-driven discovery non-dimensional…
Euler buckling (1744)
L Euler 1744 column-buckling P_cr=π²EI/L²; modern modern foundational text + Timoshenko + plate / shell + 2024 nonlinear-FEA collapse…
Nyquist-Shannon (1928-1948)
H Nyquist 1928 + C Shannon 1948 sampling-theorem; modern modern foundational text + compressed-sensing Donoho-Candes 2006 sub-Nyquist…
Channel capacity (Shannon 1948)
C Shannon 1948 C=B log₂(1+SNR) AWGN-channel; modern modern foundational text + LDPC / Polar / Turbo + Massive-MIMO + 2024 6G prediction.
Bode (1945)
H Bode 1945 'Network Analysis and Feedback Amplifier Design'; modern modern foundational text + frequency-response + control-theory…
Kalman filter detail (1960)
R Kalman 1960 + Apollo-guidance + Kalman-Bucy 1961 stochastic; modern modern foundational + EKF + UKF + particle-filter + 2024 deep-Kalman.